Sticky Note Sunflower

What you are seeing is a growth pattern of sticky notes that uses the Golden Angle (137.5 degrees) and then slowly decreases. This angle is commonly found in the plants all around us because it is an optimal angle for growth.

It was a lot of fun playing with the growth angle while creating memorizing spirals in this code, so I created a version for everyone to play with (see below):

https://editor.p5js.org/fractalkitty/present/vThUavVYE (on p5.js – sometimes this network goes down) or:

See the Pen sunflower by Sophia (@fractalkitty) on CodePen.

There is lots of fun to discover here. The fractal starts using the Golden Angle of Phi (137.5) and then decreases. You will find interesting behaviors when the angles approach numbers that divide into multiples of 360 more easily (40, 45, 60, 90, 120, 180, etc…). I wanted to do so much more, but had to stop somewhere.

If you want to know more about Phi, many mathematicians and creative types have presented it better than I (see below):

Week 2: Spiral of Theodorus

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This week the Spiral of Theodorus can be used to enhance understanding of the pythagorean theorem, right triangles, pi, and more. The spiral goes by many names (square root, Pythagorean, or Einstein Spiral) and approximates the Archimedean Spiral.

Stop animation of sketching process

Instructions:

1.) Create a right isosceles triangle where the sides that are the same measure 1 unit (I used inches).

2.) Add a 1 unit line segment perpendicular to the hypotenuse of your first triangle and then connect it to create another right triangle.

3.) Add another 1 unit line segment to the hypotenuse created in step 3 and connect it to the center to create another triangle.

4.) Repeat step 3 as many times as you wish to expand your spiral.

5.) When your done, you can transform your work into a fun sketch:

Possible reflection/discussion questions:

  • How does the Pythagorean Theorem apply here? What pattern do the hypotenuses make?
  • Can you create a function that would reflect the rate of growth for the hypotenuses?
  • There are so many ways to say “right angle” – can you say it three other ways?
  • Can you create an algorithm for making these spirals?